The STOXX 600 <.STOXX> benchmark ended up 0.4 percent with most European bourses and sectors in positive territory.
Germany's DAX <.GDAXI> rose 0.8 percent after Chancellor Angela Merkel said she would prefer a new election to minority rule after the failure of talks to form a three-way coalition.
"Financial markets did not really react too much", said Paul Donovan, chief economist at UBS Wealth Management, adding that a snap election was not the most likely option because it would be a lengthy process.
Two veteran allies of Merkel appealed to Germany's parties on Tuesday to strike compromise to form a stable government that could drag Europe's biggest economy out of a political impasse. [nL8N1NR2MR+
Volkswagen (>> Volkswagen) was among Germany's top gainers for a second day. The carmaker extended gains made after raising its mid-term outlook on Monday, rising 3 percent.
ProSiebenSat.1 (>> Prosiebensat 1 Media SE) rose 1.5 percent after JP Morgan lifted its target price to 45 euros amid continuing speculation that the German broadcaster could become an acquisition target.
Energy group Uniper (>> Uniper SE) (>> Volkswagen), meanwhile, ended flat after saying it rejected an 8.05 billion euro (£7.1 billion) bid from Finland's Fortum (>> Fortum Oyj). Uniper said the offer significantly undervalued the company.
On the UK market, a number of trading updates triggered sharp falls.
Aggreko (>> Aggreko plc), the world's largest listed temporary power provider, slumped 11 percent as the lingering effect of discounts made to win a contract in Argentina this year clouded third-quarter results.
Melrose (>> Melrose Industries) fell 5 percent after reporting difficult market conditions for its Brush business, which manufactures electricity generating equipment.
Other UK companies hit by results announcements included Mediclinic (>> Mediclinic International), down 5.8 percent, with Intertek (>> Intertek Group) falling 4.2 percent, Compass (>> Compass Group plc) 3.3 percent and Johnson Matthey (>> Johnson Matthey PLC) 3.4 percent.
Kingfisher (>> Kingfisher), Europe's largest home improvement retailer, fell as much as 1.8 percent after reporting a small fall in underlying sales, citing weak performance in France. The stock reversed losses to end up more than 1 percent.
EasyJet (>> EasyJet) was a top performer with a 5.1 percent gain after it said it was benefiting from the collapse of rivals and from problems at Ryanair (>> Ryanair Holdings plc).
Altice (>> Altice) shares fell 2.7 percent after Bank of America Merrill Lynch cut its rating on the telecoms and cable group to "neutral" from "buy", with the investment bank citing the impact of lower expectations for the company's French business.
(Reporting by Julien Ponthus and Danilo Masoni; Editing by Georgina Prodhan/Jeremy Gaunt)
By Julien Ponthus
Stocks treated in this article : Volkswagen
, Ryanair Holdings plc
, Fortum Oyj
, Intertek Group
, Mediclinic International
, Prosiebensat 1 Media SE
, Aggreko plc
, Johnson Matthey PLC
, Melrose Industries
, Uniper SE
, Compass Group plc